Solving the Richardson equations for Fermions

Abstract

Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constant interaction strength can be calculated by solving a set of non-linear coupled equations. However, in the case of Fermions these equations lead to singularities which made them very hard to solve. This letter explains how these singularities can be avoided through a change of variables making the Fermionic pairing problem numerically solvable for arbitrary single particle energies and degeneracies.

5 pages, 4 figures, submitted to Phys.Rev.C

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• Density Matrices of Seniority-Zero Geminal Wavefunctions
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• New exact solutions of the standard pairing model for well-deformed nuclei
• Spectrum and Screening cloud in the central spin model
• Effect of a Zeeman field on the superconductor-ferromagnet transition in metallic grains
• Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer
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• Density-functional theory for the pairing Hamiltonian
• A variational method for integrability-breaking Richardson-Gaudin models
• Electron-hole symmetry and solutions of Richardson pairing model
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• The multilevel pairing Hamiltonian versus the degenerate case
• The Tamm-Dancoff Approximation as the boson limit of the Richardson-Gaudin equations for pairing
• Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field
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